• Robustness properties of the M...

Result: Robustness properties of the MDF analysis of moment structures

Title:
Robustness properties of the MDF analysis of moment structures
Authors:
Shapiro, Alexander
Publisher Information:
South African Statistical Association (SASA), Pretoria
Subject Terms:
misspecified discrepancy functions, Necessary and sufficient conditions, Asymptotic distribution theory in statistics, chi-squared test statistic, asymptotic normality, asymptotic efficiency, Analysis of variance and covariance (ANOVA), covariance structures, minimum discrepancy function, MDF procedures, generalized inverse, moment structures, Linear inference, regression, robustness properties, asymptotic chi-squared distribution, MDF test statistic, linear regression, Robustness and adaptive procedures (parametric inference), least squares theory of linear models
Document Type:
Academic journal Article
File Description:
application/xml
Access URL:
https://zbmath.org/4011656
Accession Number:
edsair.c2b0b933574d..51e609c3b8463aacf81e14c6fb626623
Database:
OpenAIRE

Further Information

In this paper the robustness properties of the minimum discrepancy function (MDF) analysis of moment structures are studied. It is known that for an appropriately chosen discrepancy function the corresponding MDF test statistic is asymptotically chi-squared distributed and MDF estimators are asymptotically efficient. Unfortunately correct specification of the discrepancy function often involves estimation of huge covariance matrices. The main purpose of this paper is to investigate conditions under which the standard or slightly modified MDF procedures result in a correct statistical inference for misspecified discrepancy functions. Necessary and sufficient conditions for asymptotic chi-squared distribution of the MDF test statistics and asymptotic efficiency of the corresponding estimators are given. Interrelationship with the standard least squares theory of linear models is also discussed.